We would like to add a comment here about the relation between the VA model and a single superfield model with a linearly realized supersymmetry, where \(X\)  is not a nilpotent superfield [1]}, but the theory has \((X\bar{X})^2\)  correction to Kähler potential originating from a certain one-loop diagram, see eq. (REF ) in Appendix . The model (REF ) coincides with (REF ) with \(T=0\) , \(\alpha =1\) , \({q(t) \over 4} =-{c \over M^2}\) .
The one-loop corrections are known to lead to \(c>0\)  in the model (REF ), and to positive scalar mass squared \(m^2 = 4c {f^2\over M^2}\) . It is widely accepted that the one-loop corrections bring this model with linear supersymmetry to the VA theory with a non-linear supersymmetry. Scalars are heavy and decoupled at large positive \(c\) . In Ref. [2]} `From Linear to Non-linear SUSY' the constant \(c\)  was also taken to be positive. But in the recent paper [3]} two of the authors of [2]} decided to take \(c< 0\)  for the consistency of their ERG equations in the presence of the superfield \(T\) . This change of sign of a quartic coupling in the Kähler potential is not supported by known quantum corrections in these models, see Appendix  for details. After this change of the sign of \(c\) , the scalars in a one-superfield model with \(T=0\)  become tachyonic, and the model is no longer related to the VA theory.
